4 Numerical Analysis4.1 OverviewThe analysis package is the parent package for algorithms dealing with real-valued functions of one real variable. It contains dedicated sub-packages providing numerical root-finding, integration, interpolation and differentiation. It also contains a polynomials sub-package that considers polynomials with real coefficients as differentiable real functions. Functions interfaces are intended to be implemented by user code to represent their domain problems. The algorithms provided by the library will then operate on these function to find their roots, or integrate them, or ... Functions can be multivariate or univariate, real vectorial or matrix valued, and they can be differentiable or not. 4.2 Error handlingFor user-defined functions, when the method encounters an error during evaluation, users must use their own unchecked exceptions. The following example shows the recommended way to do that, using root solving as the example (the same construct should be used for ODE integrators or for optimizations). private static class LocalException extends RuntimeException { // the x value that caused the problem private final double x; public LocalException(double x) { this.x = x; } public double getX() { return x; } } private static class MyFunction implements UnivariateFunction { public double value(double x) { double y = hugeFormula(x); if (somethingBadHappens) { throw new LocalException(x); } return y; } } public void compute() { try { solver.solve(maxEval, new MyFunction(a, b, c), min, max); } catch (LocalException le) { // retrieve the x value } } As shown in this example the exception is really something local to user code and there is a guarantee Apache Commons Math will not mess with it. The user is safe. 4.3 Root-findingUnivariateSolver, UnivariateDifferentiableSolver and PolynomialSolver provide means to find roots of univariate real-valued functions, differentiable univariate real-valued functions, and polynomial functions respectively. A root is the value where the function takes the value 0. Commons-Math includes implementations of the several root-finding algorithms:
Some algorithms require that the initial search interval brackets the root (i.e. the function values at interval end points have opposite signs). Some algorithms preserve bracketing throughout computation and allow user to specify which side of the convergence interval to select as the root. It is also possible to force a side selection after a root has been found even for algorithms that do not provide this feature by themselves. This is useful for example in sequential search, for which a new search interval is started after a root has been found in order to find the next root. In this case, user must select a side to ensure his loop is not stuck on one root and always return the same solution without making any progress. There are numerous non-obvious traps and pitfalls in root finding. First, the usual disclaimers due to the way real world computers calculate values apply. If the computation of the function provides numerical instabilities, for example due to bit cancellation, the root finding algorithms may behave badly and fail to converge or even return bogus values. There will not necessarily be an indication that the computed root is way off the true value. Secondly, the root finding problem itself may be inherently ill-conditioned. There is a "domain of indeterminacy", the interval for which the function has near zero absolute values around the true root, which may be large. Even worse, small problems like roundoff error may cause the function value to "numerically oscillate" between negative and positive values. This may again result in roots way off the true value, without indication. There is not much a generic algorithm can do if ill-conditioned problems are met. A way around this is to transform the problem in order to get a better conditioned function. Proper selection of a root-finding algorithm and its configuration parameters requires knowledge of the analytical properties of the function under analysis and numerical analysis techniques. Users are encouraged to consult a numerical analysis text (or a numerical analyst) when selecting and configuring a solver. In order to use the root-finding features, first a solver object must be created by calling its constructor, often providing relative and absolute accuracy. Using a solver object, roots of functions are easily found using the solve methods. These methods takes a maximum iteration count maxEval, a function f, and either two domain values, min and max, or a startValue as parameters. If the maximal number of iterations count is exceeded, non-convergence is assumed and a ConvergenceException exception is thrown. A suggested value is 100, which should be plenty, given that a bisection algorithm can't get any more accurate after 52 iterations because of the number of mantissa bits in a double precision floating point number. If a number of ill-conditioned problems is to be solved, this number can be decreased in order to avoid wasting time. Bracketed solvers also take an allowed solution enum parameter to specify which side of the final convergence interval should be selected as the root. It can be ANY_SIDE, LEFT_SIDE, RIGHT_SIDE, BELOW_SIDE or ABOVE_SIDE. Left and right are used to specify the root along the function parameter axis while below and above refer to the function value axis. The solve methods compute a value c such that:
Typical usage: UnivariateFunction function = // some user defined function object final double relativeAccuracy = 1.0e-12; final double absoluteAccuracy = 1.0e-8; final int maxOrder = 5; UnivariateSolver solver = new BracketingNthOrderBrentSolver(relativeAccuracy, absoluteAccuracy, maxOrder); double c = solver.solve(100, function, 1.0, 5.0, AllowedSolution.LEFT_SIDE); Force bracketing, by refining a base solution found by a non-bracketing solver: UnivariateFunction function = // some user defined function object final double relativeAccuracy = 1.0e-12; final double absoluteAccuracy = 1.0e-8; UnivariateSolver nonBracketing = new BrentSolver(relativeAccuracy, absoluteAccuracy); double baseRoot = nonBracketing.solve(100, function, 1.0, 5.0); double c = UnivariateSolverUtils.forceSide(100, function, new PegasusSolver(relativeAccuracy, absoluteAccuracy), baseRoot, 1.0, 5.0, AllowedSolution.LEFT_SIDE); The BrentSolver uses the Brent-Dekker algorithm which is fast and robust. If there are multiple roots in the interval, or there is a large domain of indeterminacy, the algorithm will converge to a random root in the interval without indication that there are problems. Interestingly, the examined text book implementations all disagree in details of the convergence criteria. Also each implementation had problems for one of the test cases, so the expressions had to be fudged further. Don't expect to get exactly the same root values as for other implementations of this algorithm. The BracketingNthOrderBrentSolver uses an extension of the Brent-Dekker algorithm which uses inverse nth order polynomial interpolation instead of inverse quadratic interpolation, and which allows selection of the side of the convergence interval for result bracketing. This is now the recommended algorithm for most users since it has the largest order, doesn't require derivatives, has guaranteed convergence and allows result bracket selection. The SecantSolver uses a straightforward secant algorithm which does not bracket the search and therefore does not guarantee convergence. It may be faster than Brent on some well-behaved functions. The RegulaFalsiSolver is variation of secant preserving bracketing, but then it may be slow, as one end point of the search interval will become fixed after and only the other end point will converge to the root, hence resulting in a search interval size that does not decrease to zero. The IllinoisSolver and PegasusSolver are well-known variations of regula falsi that fix the problem of stuck end points by slightly weighting one endpoint to balance the interval at next iteration. Pegasus is often faster than Illinois. Pegasus may be the algorithm of choice for selecting a specific side of the convergence interval. The BisectionSolver is included for completeness and for establishing a fall back in cases of emergency. The algorithm is simple, most likely bug free and guaranteed to converge even in very adverse circumstances which might cause other algorithms to malfunction. The drawback is of course that it is also guaranteed to be slow. The UnivariateSolver interface exposes many properties to control the convergence of a solver. The accuracy properties are set at solver instance creation and cannot be changed afterwards, there are only getters to retriveve their values, no setters are available.
4.4 InterpolationA UnivariateInterpolator is used to find a univariate real-valued function f which for a given set of ordered pairs (xi,yi) yields f(xi)=yi to the best accuracy possible. The result is provided as an object implementing the UnivariateFunction interface. It can therefore be evaluated at any point, including point not belonging to the original set. Currently, only an interpolator for generating natural cubic splines and a polynomial interpolator are available. There is no interpolator factory, mainly because the interpolation algorithm is more determined by the kind of the interpolated function rather than the set of points to interpolate. There aren't currently any accuracy controls either, as interpolation accuracy is in general determined by the algorithm. Typical usage: double x[] = { 0.0, 1.0, 2.0 }; double y[] = { 1.0, -1.0, 2.0}; UnivariateInterpolator interpolator = new SplineInterpolator(); UnivariateFunction function = interpolator.interpolate(x, y); double interpolationX = 0.5; double interpolatedY = function.value(x); System.out println("f(" + interpolationX + ") = " + interpolatedY); A natural cubic spline is a function consisting of a polynomial of third degree for each subinterval determined by the x-coordinates of the interpolated points. A function interpolating N value pairs consists of N-1 polynomials. The function is continuous, smooth and can be differentiated twice. The second derivative is continuous but not smooth. The x values passed to the interpolator must be ordered in ascending order. It is not valid to evaluate the function for values outside the range x0..xN. The polynomial function returned by the Neville's algorithm is a single polynomial guaranteed to pass exactly through the interpolation points. The degree of the polynomial is the number of points minus 1 (i.e. the interpolation polynomial for a three points set will be a quadratic polynomial). Despite the fact the interpolating polynomials is a perfect approximation of a function at interpolation points, it may be a loose approximation between the points. Due to Runge's phenomenom the error can get worse as the degree of the polynomial increases, so adding more points does not always lead to a better interpolation. Loess (or Lowess) interpolation is a robust interpolation useful for smoothing univariate scaterplots. It has been described by William Cleveland in his 1979 seminal paper Robust Locally Weighted Regression and Smoothing Scatterplots. This kind of interpolation is computationally intensive but robust. Microsphere interpolation is a robust multidimensional interpolation algorithm. It has been described in William Dudziak's MS thesis. Hermite interpolation is an interpolation method that can use derivatives in addition to function values at sample points. The HermiteInterpolator class implements this method for vector-valued functions. The sampling points can have any spacing (there are no requirements for a regular grid) and some points may provide derivatives while others don't provide them (or provide derivatives to a smaller order). Points are added one at a time, as shown in the following example: HermiteInterpolator interpolator = new HermiteInterpolator; // at x = 0, we provide both value and first derivative interpolator.addSamplePoint(0.0, new double[] { 1.0 }, new double[] { 2.0 }); // at x = 1, we provide only function value interpolator.addSamplePoint(1.0, new double[] { 4.0 }); // at x = 2, we provide both value and first derivative interpolator.addSamplePoint(2.0, new double[] { 5.0 }, new double[] { 2.0 }); // should print "value at x = 0.5: 2.5625" System.out.println("value at x = 0.5: " + interpolator.value(0.5)[0]); // should print "derivative at x = 0.5: 3.5" System.out.println("derivative at x = 0.5: " + interpolator.derivative(0.5)[0]); // should print "interpolation polynomial: 1 + 2 x + 4 x^2 - 4 x^3 + x^4" System.out.println("interpolation polynomial: " + interpolator.getPolynomials()[0]); A BivariateGridInterpolator is used to find a bivariate real-valued function f which for a given set of tuples (xi,yj,fij) yields f(xi,yj)=fij to the best accuracy possible. The result is provided as an object implementing the BivariateFunction interface. It can therefore be evaluated at any point, including a point not belonging to the original set. The arrays xi and yj must be sorted in increasing order in order to define a two-dimensional grid. In bicubic interpolation, the interpolation function is a 3rd-degree polynomial of two variables. The coefficients are computed from the function values sampled on a grid, as well as the values of the partial derivatives of the function at those grid points. From two-dimensional data sampled on a grid, the BicubicSplineInterpolator computes a bicubic interpolating function. Prior to computing an interpolating function, the SmoothingPolynomialBicubicSplineInterpolator class performs smoothing of the data by computing the polynomial that best fits each of the one-dimensional curves along each of the coordinate axes. A TrivariateGridInterpolator is used to find a trivariate real-valued function f which for a given set of tuples (xi,yj,zk, fijk) yields f(xi,yj,zk)=fijk to the best accuracy possible. The result is provided as an object implementing the TrivariateFunction interface. It can therefore be evaluated at any point, including a point not belonging to the original set. The arrays xi, yj and zk must be sorted in increasing order in order to define a three-dimensional grid. In tricubic interpolation, the interpolation function is a 3rd-degree polynomial of three variables. The coefficients are computed from the function values sampled on a grid, as well as the values of the partial derivatives of the function at those grid points. From three-dimensional data sampled on a grid, the TricubicSplineInterpolator computes a tricubic interpolating function. 4.5 IntegrationA UnivariateIntegrator provides the means to numerically integrate univariate real-valued functions. Commons-Math includes implementations of the following integration algorithms: 4.6 PolynomialsThe org.apache.commons.math4.analysis.polynomials package provides real coefficients polynomials. The PolynomialFunction class is the most general one, using traditional coefficients arrays. The PolynomialsUtils utility class provides static factory methods to build Chebyshev, Hermite, Jacobi, Laguerre and Legendre polynomials. Coefficients are computed using exact fractions so these factory methods can build polynomials up to any degree. 4.7 DifferentiationThe org.apache.commons.math4.analysis.differentiation package provides a general-purpose differentiation framework. The core class is DerivativeStructure which holds the value and the differentials of a function. This class handles some arbitrary number of free parameters and arbitrary derivation order. It is used both as the input and the output type for the UnivariateDifferentiableFunction interface. Any differentiable function should implement this interface. The main idea behind the DerivativeStructure class is that it can be used almost as a number (i.e. it can be added, multiplied, its square root can be extracted or its cosine computed... However, in addition to computed the value itself when doing these computations, the partial derivatives are also computed alongside. This is an extension of what is sometimes called Rall's numbers. This extension is described in Dan Kalman's paper Doubly Recursive Multivariate Automatic Differentiation, Mathematics Magazine, vol. 75, no. 3, June 2002. Rall's numbers only hold the first derivative with respect to one free parameter whereas Dan Kalman's derivative structures hold all partial derivatives up to any specified order, with respect to any number of free parameters. Rall's numbers therefore can be seen as derivative structures for order one derivative and one free parameter, and primitive real numbers can be seen as derivative structures with zero order derivative and no free parameters. The workflow of computation of a derivatives of an expression y=f(x) is the following one. First we configure an input parameter x of type DerivativeStructure so it will drive the function to compute all derivatives up to order 3 for example. Then we compute y=f(x) normally by passing this parameter to the f function.At the end, we extract from y the value and the derivatives we want. As we have specified 3rd order when we built x, we can retrieve the derivatives up to 3rd order from y. The following example shows that (the 0 parameter in the DerivativeStructure constructor will be explained in the next paragraph): int params = 1; int order = 3; double xRealValue = 2.5; DerivativeStructure x = new DerivativeStructure(params, order, 0, xRealValue); DerivativeStructure y = f(x); System.out.println("y = " + y.getValue(); System.out.println("y' = " + y.getPartialDerivative(1); System.out.println("y'' = " + y.getPartialDerivative(2); System.out.println("y''' = " + y.getPartialDerivative(3); In fact, there are no notions of variables in the framework, so neither x nor y are considered to be variables per se. They are both considered to be functions and to depend on implicit free parameters which are represented only by indices in the framework. The x instance above is there considered by the framework to be a function of free parameter p0 at index 0, and as y is computed from x it is the result of a functions composition and is therefore also a function of this p0 free parameter. The p0 is not represented by itself, it is simply defined implicitely by the 0 index above. This index is the third argument in the constructor of the x instance. What this constructor means is that we built x as a function that depends on one free parameter only (first constructor argument set to 1), that can be differentiated up to order 3 (second constructor argument set to 3), and which correspond to an identity function with respect to implicit free parameter number 0 (third constructor argument set to 0), with current value equal to 2.5 (fourth constructor argument set to 2.5). This specific constructor defines identity functions, and identity functions are the trick we use to represent variables (there are of course other constructors, for example to build constants or functions from all their derivatives if they are known beforehand). From the user point of view, the x instance can be seen as the x variable, but it is really the identity function applied to free parameter number 0. As the identity function, it has the same value as its parameter, its first derivative is 1.0 with respect to this free parameter, and all its higher order derivatives are 0.0. This can be checked by calling the getValue() or getPartialDerivative() methods on x. When we compute y from this setting, what we really do is chain f after the identity function, so the net result is that the derivatives are computed with respect to the indexed free parameters (i.e. only free parameter number 0 here since there is only one free parameter) of the identity function x. Going one step further, if we compute z = g(y), we will also compute z as a function of the initial free parameter. The very important consequence is that if we call z.getPartialDerivative(1), we will not get the first derivative of g with respect to y, but with respect to the free parameter p0: the derivatives of g and f will be chained together automatically, without user intervention. This design choice is a very classical one in many algorithmic differentiation frameworks, either based on operator overloading (like the one we implemented here) or based on code generation. It implies the user has to bootstrap the system by providing initial derivatives, and this is essentially done by setting up identity function, i.e. functions that represent the variables themselves and have only unit first derivative. This design also allow a very interesting feature which can be explained with the following example. Suppose we have a two arguments function f and a one argument function g. If we compute g(f(x, y)) with x and y be two variables, we want to be able to compute the partial derivatives dg/dx, dg/dy, d2g/dx2 d2g/dxdy d2g/dy2. This does make sense since we combined the two functions, and it does make sense despite g is a one argument function only. In order to do this, we simply set up x as an identity function of an implicit free parameter p0 and y as an identity function of a different implicit free parameter p1 and compute everything directly. In order to be able to combine everything, however, both x and y must be built with the appropriate dimensions, so they will both be declared to handle two free parameters, but x will depend only on parameter 0 while y will depend on parameter 1. Here is how we do this (note that getPartialDerivative is a variable arguments method which take as arguments the derivation order with respect to all free parameters, i.e. the first argument is derivation order with respect to free parameter 0 and the second argument is derivation order with respect to free parameter 1): int params = 2; int order = 2; double xRealValue = 2.5; double yRealValue = -1.3; DerivativeStructure x = new DerivativeStructure(params, order, 0, xRealValue); DerivativeStructure y = new DerivativeStructure(params, order, 1, yRealValue); DerivativeStructure f = DerivativeStructure.hypot(x, y); DerivativeStructure g = f.log(); System.out.println("g = " + g.getValue(); System.out.println("dg/dx = " + g.getPartialDerivative(1, 0); System.out.println("dg/dy = " + g.getPartialDerivative(0, 1); System.out.println("d2g/dx2 = " + g.getPartialDerivative(2, 0); System.out.println("d2g/dxdy = " + g.getPartialDerivative(1, 1); System.out.println("d2g/dy2 = " + g.getPartialDerivative(0, 2); There are several ways a user can create an implementation of the UnivariateDifferentiableFunction interface. The first method is to simply write it directly using the appropriate methods from DerivativeStructure to compute addition, subtraction, sine, cosine... This is often quite straigthforward and there is no need to remember the rules for differentiation: the user code only represent the function itself, the differentials will be computed automatically under the hood. The second method is to write a classical UnivariateFunction and to pass it to an existing implementation of the UnivariateFunctionDifferentiator interface to retrieve a differentiated version of the same function. The first method is more suited to small functions for which user already control all the underlying code. The second method is more suited to either large functions that would be cumbersome to write using the DerivativeStructure API, or functions for which user does not have control to the full underlying code (for example functions that call external libraries). Apache Commons Math provides one implementation of the UnivariateFunctionDifferentiator interface: FiniteDifferencesDifferentiator. This class creates a wrapper that will call the user-provided function on a grid sample and will use finite differences to compute the derivatives. It takes care of boundaries if the variable is not defined on the whole real line. It is possible to use more points than strictly required by the derivation order (for example one can specify an 8-points scheme to compute first derivative only). However, one must be aware that tuning the parameters for finite differences is highly problem-dependent. Choosing the wrong step size or the wrong number of sampling points can lead to huge errors. Finite differences are also not well suited to compute high order derivatives. Here is an example on how this implementation can be used: // function to be differentiated UnivariateFunction basicF = new UnivariateFunction() { public double value(double x) { return x * FastMath.sin(x); } }); // create a differentiator using 5 points and 0.01 step FiniteDifferencesDifferentiator differentiator = new FiniteDifferencesDifferentiator(5, 0.01); // create a new function that computes both the value and the derivatives // using DerivativeStructure UnivariateDifferentiableFunction completeF = differentiator.differentiate(basicF); // now we can compute display the value and its derivatives // here we decided to display up to second order derivatives, // because we feed completeF with order 2 DerivativeStructure instances for (double x = -10; x < 10; x += 0.1) { DerivativeStructure xDS = new DerivativeStructure(1, 2, 0, x); DerivativeStructure yDS = f.value(xDS); System.out.format(Locale.US, "%7.3f %7.3f %7.3f%n", yDS.getValue(), yDS.getPartialDerivative(1), yDS.getPartialDerivative(2)); } Note that using FiniteDifferencesDifferentiatora> in order to have a UnivariateDifferentiableFunction that can be provided to a Newton-Raphson's solver is a very bad idea. The reason is that finite differences are not really accurate and needs lots of additional calls to the basic underlying function. If user initially have only the basic function available and needs to find its roots, it is much more accurate and much more efficient to use a solver that only requires the function values and not the derivatives. A good choice is to use bracketing nth order Brent method, which in fact converges faster than Newton-Raphson's and can be configured to a highere order (typically 5) than Newton-Raphson which is an order 2 method. Another implementation of the UnivariateFunctionDifferentiator interface is under development in the related project Apache Commons Nabla. This implementation uses automatic code analysis and generation at binary level. However, at time of writing (end 2012), this project is not yet suitable for production use. |


The angular-datatables
also provides an API in order to make the plugin ColumnFilter
work with datatables.
You need to add the file angular-datatables.columnfilter.min.js
to your HTML file.
You also need to add the dependency datatables.columnfilter
to your Angular app.
See the API for the complete list of methods of the helper.


Nov. 24 (UPI) -- Taylor Swift won big at the 47th annual American Music Awards on Sunday, taking home the award for Artist of the Year.
"I'm lucky to be here, I know that every step of the way," Swift said while accepting the award. Drake, Ariana Grande, Halsey and Post Malone were also nominated for the award.
Swift has now won more AMAs than any other artist in history.
Swift was also honored with the prestigious Artist of the Decade Award, which was presented by music legend Carole King.
The pop star unleashed a career-spanning concert, performing "The Man," "Love Story," "I Knew You Were Trouble," "Blank Space," and "Shake It Off," which also featured Camila Cabello and Halsey.
Swift ended the celebration with a piano version of "Lover," the title track from her latest album which won the AMA for Favorite Album - Pop/Rock.
Shania Twain gave the last performance of the night, singing Swift's "Shake It Off" and Drake's "God's Plan" before launching into her songs "You're Still The One," "Any Man Of Mine" and "Man! I Feel Like A Woman," among others.
Dan + Shay won Favorite Song - Country for "Speechless." Dua Lipa performed her new track, "Don't Start Now" while silver balloons fell upon the audience.
Malone performed his song "Circles" before he was joined onstage by Ozzy Osbourne, Travis Scott and WATT. Aguilera teamed up with A Great Big World for "Fall on Me."
Lil Nas X won Favorite Song - Rap/Hip-Hop for "Old Town Road" featuring Billy Ray Cyrus.
Earlier, the Jonas Brothers performed "Only Human" from their tour in Boston in front of a sold-out crowd.
Post Malone took home the award for Favorite Album - Rap/Hip-Hop for Hollywood's Bleeding. Meek Mill for Championships and Travis Scott for Astroworld were also nominated.
Green Day celebrated the 25th anniversary of their album Dookie and performed "Basket Case."
Eilish brought fire to the stage for "All The Good Girls Go To Hell," the first AMA performance of her career. Eilish then won New Artist of the Year shortly after. Lizzo, Luke Combs, Lil Nas X and Ella Mai were also nominated.
Eilish won the first award of the night, Favorite Artist - Alternative Rock. Imagine Dragons and Panic! At The Disco were also nominated.
Carrie Underwood won Favorite Album - Country for Cry Pretty. Underwood was then surprised with winning Favorite Female Artist - Country when she reached the stage. BTS won Tour of the Year, speaking to fans through a video as they were not present at the event.
Kesha gave a church-themed performance of "Raising Hell" before she launched into her party anthem "Tik Tok." Toni Braxton returned to the AMAs and performed her classic song, "Un-Break My Heart."
Shawn Mendes and Cabello teamed up for "Senorita."  "Senorita"would go on to win Collaboration of the Year.
Cabello returned later and gave a solo performance of "Living Proof."
Lizzo, in a red dress, performed "Jerome" which was followed by Thomas Rhett singing "Look What God Gave Her." The country star walked down to the audience for part of the song.
Halsey won Favorite Song - Pop/Rock for "Without Me." The 25-year-old also performed "Graveyard" during the ceremony.
Selena Gomez opened the show with a performance of her new single "Lose You To Love Me" before she brought out backup dancers and changed her outfit for "Look At Her Now."
Ciara, who hosted the show, performed her new song, "Melanin."
The AMAs aired live from the Microsoft Theater in Los Angeles.


Baseball Hat
I love baseball hats. I wear them everyday. YAY! for baseball!
Beret
oh... je suis french.
Cowboy Hat
I love cows


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is an objective way to create and manage object's structure and behavior with jQuery.
the definition of gbutton is part of the edison library
$.engineer.make( object_type, [options] )
jQuery.engineer allows you to define reusable objects structure and behavior.
were all created using same definition but with different options. To make new engineer objects use the make() method. The make() method optionally takes a second arguments which is the options passed into the objects definition.
$.engineer.define( object_type, definition )
Let's have a look at the definition. Each definition can have 3 parts: structure, behavior and defaults. But none of them are required.
Structure: function([options]) { return object; }
Structure is defined as a function that can optionally take on parameter for options. What ever is returned from the structure function will be the objects DOM element(s). In the example above the structure function returns a div:
Behavior: function([options]) { return methods; }
Behavior is also defined as a function. The context of the behavior function is the jQuery object returned by the structure function. No need to wrap this in $(). Since this is already a jQuery object it's easy to bind events to your element. Notice that the elements created above all have a click function bound to them. Scroll up and give it a try.
The behavior function can return methods that can be invoke later. More on this in the Object Methods section.
Defaults:
You may have noticed both the structure and behavior functions both take a single parameter: options. Defaults set up the default options that are passed into structure and behavior. You can override these by passing new options when you create your element. These new options will be merged into your defaults.
Object Methods
jQuery.engineer allows you to define methods on elements.
The object returned by the behavior function is an objects methods. For example if I wanted the method 'blink' on an element' I would do the following:
I define 'blink' on a object which is then return by the behavior function.
$().send(method, [arg1, [arg2, [etc..]]])
To invoke methods you just defined use send(). The send() method on all jQuery objects. If the object does not have a method it will not error so you can pass groups of objects public methods without worry. Lets looks at an example. The button below will try to invoke the 'blink' method on all divs, but only the divs below the button have 'blink' defined.
Below is the code that creates the button above.
Send can also pass arguments to methods. If a public method takes arguments add them to the arguments you give send. For Rubyists this is a lot like the ruby send method.
$().behaveLike(object_type, [options])
Notice in the example above I don't define defaults or a structure. This is because I only want to use this definition to add behavior to elements. You can add the behavior of any engineer object to any jQuery object by using the behaveLike() function. So to make some element have the method 'blink' I would do something like:
Lets give this a try. The button to the right will call send('blink') on all paragraph elements. The button to the left will add the method 'blink' to all paragraph elements using the behaveLike() method.
$.engineer.build(object_type, [options])
If you only want the structure of a engineer objects you can use the build() method. Below I've only created the structure of the button not the behavior.
$().makeInto(object_type);
If you'd like to take some existing DOM elements and make them into jQuery engineer objects you can use the makeInto() method.
You don't need to pass any options into makeInto. For each option defined in defaults, makeInto will take the xhtml attributes of the elements as it's options.
The button above uses makeInto to replace the elements with new jQuery engineer objects. The definition for 'gbutton_link' is below:


{% extends "base.html" %} {% import "bootstrap/wtf.html" as wtf %} {% import "bootstrap/fixes.html" as fixes %} {% import "bootstrap/utils.html" as util %} {% import "macros.html" as pbw %} {% block title %}Citation{% endblock %} {% block content %}
{{ evidence.text }}


TabDisplayer and TabbedControl
This package contains two gui components:
- TabDisplayer - A component which displays tabs, the contents of which are defined in a
TabDataModel
. This can be used as a standalone component for tab-driven navigation. It has several UI styles available to suit different purposes, such as scrollable tabs, fixed width tabs, or toggle buton tabs.
- TabbedContainer - A component which also takes a
TabDataModel
, which offers similar functionality to a JTabbedPane, and (as an implementation detail) embeds a TabDisplayer to display its tabs.
Where these classes differ from JTabbedPane is as follows:
- Fully model driven - the contents of the AWT hierarchy are an artifact, not the primary source of information about the contents of the tabbed container. Several policies are available for when components to be displayed in tabs are to be physically added to a container
- Multiple UI styles supported up front - Several different UI styles are supported, with UI delegates for the major look and feels.
- Drag and drop visualization support - while the actual functionality of what to drag and what to do with it is left up to the application, there is built in support for creating drag images of tabs and visual feedback for where a tab will be placed if dropped.
- Support for using a single component across multiple tabs is designed in - there are some hacks one can do which (maybe) will allow a JTabbedPane to do this, but they are not recommended. This is made easy using the
ComponentConverter
class, which determines how an element in the data model is translated into a GUI component
- Very granular event model - TabDataModel is designed on the assumption that the application may atomically add/remove/modify discontiguous ranges of tabs, their contents, titles or icons, and that such operations should be handled atomically, generating a single event/repaint
Besides this module the org.netbeans.swing.popupswitcher
package is used from core/windows too. Classes contained in the package are
rather general and therefore this package could be moved in the future. It is
placed here only due to current modules dependencies. Consequently the package
is not intended for external use.


Author | Dengqi
Currently a undergraduate student in ShanghaiTech University
上海科技大學信息學院，本科在讀。電子工程專業。
Life is not easy.


FUNDAMENTAL ADHESIVE STUDIES OF BLOCK COPOLYMERS by
Margaret Mary Sheridan
Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in
Chemistry
APPROVED:
—
T.C. Ward, Chairman
D.W. Dwight “WK Oglioruso
ee Ee J.E. McGrath J.Pé/Wightman
October, 1985
Blacksburg, Virginia


This is BEFORE TEXT
Key
Summary
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DUMMY-1
]
Dummy Issue
[
DUMMY-4
]
Dummy Issue
[
DUMMY-3
]
Dummy Issue
[
DUMMY-2
]
Dummy Issue
This is AFTER TEXT


Clustering sequences into OTUs using q2-vsearch¶
De novo, closed-reference, and open-reference clustering are currently supported in QIIME 2.
Clustering of sequences or features into OTUs using vsearch is currently
possible from demultiplexed, quality-controlled sequence data (i.e., a
SampleData[Sequences]
artifact), or from dereplicated, quality-controlled
data in feature table and feature representative sequences (i.e., the
FeatureTable[Frequency]
and FeatureData[Sequence]
artifacts, which
could be generated using the qiime dada2 denoise-*
or qiime deblur
denoise-*
commands). The first option is currently performed in two steps
(but will likely be accessible through a single command in the future for
convenience). The second option is performed in one step.
QIIME 1 Users
Demultiplexed, quality-filtered sequence data is synonymous with the
seqs.fna
file, generated by the QIIME 1 split_libraries*.py
commands.
After working through this tutorial, you will know how to run de novo,
closed-reference, and open-reference clustering. This will be illustrated
beginning with a QIIME 1 seqs.fna
file that will be read into an
SampleData[Sequences]
artifact. If you already have
FeatureTable[Frequency]
and FeatureData[Sequence]
artifacts that you’d
like to cluster, you can skip ahead to the Clustering of FeatureTable[Frequency] and FeatureData[Sequence]
section of this tutorial.
Obtain the data¶
Start by creating a directory to work in.
mkdir qiime2-otu-clustering-tutorial
cd qiime2-otu-clustering-tutorial
Next, download the necessary files:
Download URL: https://data.qiime2.org/2019.7/tutorials/otu-clustering/seqs.fna
Save as: seqs.fna
wget \
-O "seqs.fna" \
"https://data.qiime2.org/2019.7/tutorials/otu-clustering/seqs.fna"
curl -sL \
"https://data.qiime2.org/2019.7/tutorials/otu-clustering/seqs.fna" > \
"seqs.fna"
Download URL: https://data.qiime2.org/2019.7/tutorials/otu-clustering/85_otus.qza
Save as: 85_otus.qza
wget \
-O "85_otus.qza" \
"https://data.qiime2.org/2019.7/tutorials/otu-clustering/85_otus.qza"
curl -sL \
"https://data.qiime2.org/2019.7/tutorials/otu-clustering/85_otus.qza" > \
"85_otus.qza"
Dereplicating a SampleData[Sequences]
artifact¶
If you are beginning your analysis with demultiplexed, quality controlled
sequences, such as those in a QIIME 1 seqs.fna
file your first step
is to import that data into a QIIME 1 artifact. The semantic type used here is
SampleData[Sequences]
, indicating that the data represents collections of
sequences associated with one or more samples.
qiime tools import \
--input-path seqs.fna \
--output-path seqs.qza \
--type 'SampleData[Sequences]'
After importing data, you can dereplicate it with the dereplicate-sequences
command.
qiime vsearch dereplicate-sequences \
--i-sequences seqs.qza \
--o-dereplicated-table table.qza \
--o-dereplicated-sequences rep-seqs.qza
The outputs from dereplicate-sequences
are a FeatureTable[Frequency]
artifact and a FeatureData[Sequence]
artifact. The
FeatureTable[Frequency]
artifact is the feature table indicating the number
of times each amplicon sequence variant (ASV) is observed in each of your
samples. The FeatureData[Sequence]
contains the mapping of each feature
identifier to the sequence variant that defines that feature. These files are
analogous to those generated by qiime dada2 denoise-*
and qiime deblur
denoise-*
, except that no denoising, chimera removal, or other quality
control has been applied in the dereplication process. (In this example, the
only quality control of these data is what was applied outside of QIIME 2,
before the import
step.)
Clustering of FeatureTable[Frequency]
and FeatureData[Sequence]
¶
OTU clustering in QIIME 2 is currently applied to a FeatureTable[Frequency]
artifact and a FeatureData[Sequence]
artifact. These artifacts can come
from a variety of analysis pipelines, including qiime vsearch
dereplicate-sequences
(illustrated above), qiime dada2 denoise-*
, qiime
deblur denoise-*
, or one of the clustering processes illustrated below (for
example, to recluster data at a lower percent identity).
The sequences in the FeatureData[Sequence]
artifact are clustered against
one another (in de novo clustering) or a reference database (in
closed-reference clustering), and then features in the FeatureTable
are
collapsed, resulting in new features that are clusters of the input features.
De novo clustering¶
De novo clustering of a feature table can be performed as follows. In this example, clustering is performed at 99% identity to create 99% OTUs.
qiime vsearch cluster-features-de-novo \
--i-table table.qza \
--i-sequences rep-seqs.qza \
--p-perc-identity 0.99 \
--o-clustered-table table-dn-99.qza \
--o-clustered-sequences rep-seqs-dn-99.qza
The outputs from this process are a FeatureTable[Frequency]
artifact and a
FeatureData[Sequence]
artifact. The FeatureData[Sequence]
artifact will
contain the centroid sequence defining each OTU cluster.
Closed-reference clustering¶
Closed-reference clustering of a feature table can be performed as follows. In
this example, clustering is performed at 85% identity against the Greengenes
13_8 85% OTUs reference database. The reference database is provided as a
FeatureData[Sequence]
artifact.
Note
Closed-reference OTU clustering is generally performed at a higher percent identity, but 85% is used here so users of this tutorial don’t have to download a larger reference database. Typically clustering at some percent identity is performed against a reference database clustered at the same percent identity, but this has not been properly benchmarked to determine if it is the optimal way to perform closed-reference clustering.
qiime vsearch cluster-features-closed-reference \
--i-table table.qza \
--i-sequences rep-seqs.qza \
--i-reference-sequences 85_otus.qza \
--p-perc-identity 0.85 \
--o-clustered-table table-cr-85.qza \
--o-clustered-sequences rep-seqs-cr-85.qza \
--o-unmatched-sequences unmatched-cr-85.qza
Output artifacts:
The outputs from cluster-features-closed-reference
are a
FeatureTable[Frequency]
artifact and a FeatureData[Sequence]
artifact.
The FeatureData[Sequence]
artifact in this case is not the sequences
defining the features in the FeatureTable
, but rather the collection of
feature ids and their sequences that didn’t match the reference database at 85%
identity. The reference sequences provided as input should be used as sequences
defining the features in the FeatureTable
in closed-reference OTU picking.
Open-reference clustering¶
Like the closed-reference clustering example above, open-reference clustering
can be performed using the qiime vsearch cluster-features-open-reference
command.
Note
Open-reference OTU clustering is generally performed at a higher percent identity, but 85% is used here so users of this tutorial don’t have to download a larger reference database. Typically clustering at some percent identity is performed against a reference database clustered at the same percent identity, but this has not been properly benchmarked to determine if it is the optimal way to perform open-reference clustering.
qiime vsearch cluster-features-open-reference \
--i-table table.qza \
--i-sequences rep-seqs.qza \
--i-reference-sequences 85_otus.qza \
--p-perc-identity 0.85 \
--o-clustered-table table-or-85.qza \
--o-clustered-sequences rep-seqs-or-85.qza \
--o-new-reference-sequences new-ref-seqs-or-85.qza
Output artifacts:
The outputs from cluster-features-open-reference
are a
FeatureTable[Frequency]
artifact and two FeatureData[Sequence]
artifacts. One of the FeatureData[Sequence]
artifacts represents the
clustered sequences, while the other artifact represents the new reference
sequences, composed of the reference sequences used for input, as well as the
sequences clustered as part of the internal de novo clustering step.


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Source code for pymaancrypt.blockmodes
# -*- coding: utf-8 -*-
import math
from . import mathfuncs
class __DummyEncryptor__:
"""
This dummy encryptor is only used for testing purposes and does not actually perform any encryption.
"""
def encrypt(self, data, keyobj):
return data
def decrypt(self, data, keyobj):
return data
[docs]class BaseBlockMode(object):
"""
Base class for all block modes
"""
def __init__(self, encryptor, maxBlockLength):
"""
Constructor
"""
self.encryptor = encryptor
self.blockLengthBits = mathfuncs.floorPowerOf( maxBlockLength, 2 )
self.blockLengthBytes = int(self.blockLengthBits / 8)
if self.blockLengthBits < 8:
raise AssertionError("Max Block Length must be larger than 8 bits (one byte)")
[docs] def encryptFromString(self, data, keyobj):
"""
Convenience method for encrypting a string of data, return type is bytearray
"""
return self.encryptByteArray(bytearray(data, 'utf-8'), keyobj)
[docs] def decryptToString(self, data, keyobj):
"""
Convenience method for decrypting a bytearray, return type is utf-8 encoded string
"""
return self.decryptByteArray(data, keyobj).decode().split('\x00')[0]
[docs] def encryptByteArray(self, data, keyobj):
"""
Encryption method
"""
raise NotImplementedError("Is abstract")
[docs] def decryptByteArray(self, data, keyobj):
"""
Decryption method
"""
raise NotImplementedError("Is abstract")
[docs]class ECB(BaseBlockMode):
"""
Electronic code book block encryption scheme, this is the least secure of all
block modes and should only be used for educational purposes
"""
def __init__(self, encryptor, maxBlockLength):
"""
Constructor
"""
super().__init__(encryptor, maxBlockLength)
[docs] def encryptByteArray(self, data, keyobj):
"""
Encrypts a variable length bytearray with the provided encryptor with the ECB
block scheme.
padding will be all zeroes due to the fact that encryption expects
a c-style string as payload
>>> if True:
... e = __DummyEncryptor__()
... ecb = ECB(e, 32)
... c = ecb.encryptFromString('This is a test', None)
... c.decode()
'This is a test\\x00\\x00'
"""
nrOfBlocks = int(math.ceil(len(data)/self.blockLengthBytes))
C = bytearray()
for i in range(nrOfBlocks):
m = bytearray(self.blockLengthBytes)
for j in range(self.blockLengthBytes):
index = i*self.blockLengthBytes+j
if index < len(data):
m[j] = data[index]
c = self.encryptor.encrypt(m, keyobj)
if len(c) != self.blockLengthBytes:
raise AssertionError("Encryptor is not symmetric! "+
"Block Cipher modes require encryptors "+
"with equal length of input & output blocks.")
for cb in c:
C.append(cb)
return C
[docs] def decryptByteArray(self, data, keyobj):
"""
Decrypts a variable length bytearray with the provided encryptor with the ECB
block scheme.
>>> if True:
... e = __DummyEncryptor__()
... ecb = ECB(e, 32)
... ecb.decryptToString(bytearray('This is a test\\x00\\x00', 'utf-8'), None)
'This is a test'
"""
nrOfBlocks = int(math.ceil(len(data)/self.blockLengthBytes))
M = bytearray()
for i in range(nrOfBlocks):
c = bytearray(self.blockLengthBytes)
for j in range(self.blockLengthBytes):
index = i*self.blockLengthBytes+j
if index < len(data):
c[j] = data[index]
m = self.encryptor.decrypt(c, keyobj)
for mb in c:
M.append(mb)
return M
[docs]def testmodule():
"""
Should return (#failed, #tried)
"""
import doctest
import sys
thismodule = sys.modules[__name__]
return doctest.testmod(m=thismodule)
if __name__ == "__main__":
if testmodule()[0] == 0:
print("Success!")